Electromagnetically induced transparency (EIT) is a phenomenon that is now well known in the art. EIT employs a medium (e.g. strontium vapor or lead vapor) that has an absorbing atomic transition. The medium strongly absorbs light resonant with the atomic transition. In other words, the medium is opaque to a light beam resonant with the atomic transition. In the method of EIT, light of a second frequency (a coupling beam), prevents the medium from absorbing light of the resonant frequency (a probe beam). In addition, it prevents the medium from imparting an excess phase shift to the probe beam. The medium is thereby rendered transparent to the probe beam. Light of the coupling beam induces the medium to become transparent to light of the probe beam.
FIG. 1 shows an energy level diagram of an atom capable of experiencing EIT. Level .vertline.1&gt; may be a ground level for the atom, (as is the case of .sup.208 Pb vapor). Transition 20 between level .vertline.1&gt; and level .vertline.2&gt; is a dipole forbidden transition. Electrons in level .vertline.2&gt; cannot decay to level .vertline.1&gt; via an electric dipole transition. Instead, electrons in level .vertline.2&gt; decay to level .vertline.1&gt; via much slower quadrupole and two-photon transitions. Level .vertline.2&gt; is known as a metastable level. Transitions 22, 24, are dipole allowed between levels .vertline.2&gt; and .vertline.3&gt;, and between levels .vertline.1&gt; and .vertline.3&gt;. These transitions 22, 24 can be induced by an external dipole electric field.
In EIT, the coupling beam is resonant with transition 22, and the probe beam is resonant with transition 24. Application of the coupling beam causes transition 24 to be unable to absorb the probe beam. FIG. 2 illustrates why this is so. FIG. 2 shows the energy level diagram of a dressed atom; the energy levels have been modified by the application of the coupling beam. The coupling beam mixes levels .vertline.2&gt; and .vertline.3&gt; to produce new levels .vertline.3a&gt; and .vertline.3b&gt;. Levels .vertline.3a&gt; and .vertline.3b&gt; are equally separated from the original position of level .vertline.3&gt;, and are separated from each other by a spitting energy 26. The splitting energy 26 is equal to a Rabi frequency, Q, of the coupling laser, which is defined as follows: ##EQU1##
Where .mu..sub.23 is the dipole matrix element or coupling coefficient (a fundamental property of the atomic species), E is the electric field of the coupling beam, and h is Planck's constant.
Therefore, the Rabi frequency and the splitting energy 26, are controllable by adjusting the intensity of the coupling beam: EQU .OMEGA..varies..sqroot.I
Where I is the intensity of the coupling beam. In the dressed atom, transition .vertline.1&gt; to .vertline.3a&gt; and transition .vertline.1&gt; to .vertline.3b&gt; are absorbing and separated in energy by the Rabi frequency. However, when the probe beam is tuned into resonance with transition 24 (.vertline.1&gt; to midway between states .vertline.3a&gt; and .vertline.3b&gt;), zero absorption occurs. Due to the proximity of levels .vertline.3a&gt; and .vertline.3b&gt; to level .vertline.3&gt;, one would expect some absorption of the probe beam by levels .vertline.3a&gt; and .vertline.3b&gt;. This does not happen, however, because levels .vertline.3a&gt; and .vertline.3b&gt; exhibit a destructive quantum interference in the absorption profile. This destructive quantum interference prevents any electron from decaying from levels .vertline.3a&gt; and .vertline.3b&gt; to any other level in the atom. Therefore, when the medium is exposed to the coupling beam, and the probe beam is tuned to transition 24, the atoms cannot absorb energy from the probe beam, and the probe beam passes through the medium relatively unaffected. FIG. 3 is a graph illustrating the absorption spectrum of the medium with the coupling beam and without the coupling beam.
If the probe beam is not applied, then level .vertline.2&gt; is empty. Application of the coupling and probe beam results in level .vertline.2&gt; becoming populated. Atoms with both level .vertline.2&gt; and level .vertline.1&gt; populated may behave as local oscillators, capable of mixing with optical frequencies to produce sum and difference frequencies (similar to the practice of signal mixing in the radiofrequency arts). This effect provides the basis for many nonlinear optical effects, including nonlinear frequency generation. Reference can be made to U.S. Pat. No. 5,771,117 to Harris et al. concerning this application of EIT.
Previous applications of EIT have often relied upon the use of isotopically pure materials, which are very expensive. As a specific example, it is known in the art that .sup.208 Pb can be used in EIT applications. .sup.208 Pb, however, costs about $5,000 per gram, and several grams are often necessary to produce a useful EIT nonlinear optical device. The reason that isotopically pure materials are necessary is that different isotopes have different energy level structures. Therefore, in isotopically mixed materials, the coupling and probe beams cannot be tuned to be resonant with all the atoms. Atoms slightly off resonance with the coupling beam will absorb the probe beam, thereby preventing complete transparency, and impart additional phase on the probe beam.
Different isotopic species often have different energy levels due to the phenomenon of hyperfine splitting. Hyperfine splitting occurs when the nucleus of an atom has nonzero nuclear spin and hence a nonzero magnetic moment. The magnetic moment of the nucleus causes some electron energy levels (i.e. energy levels with nonzero total angular momentum, J.notident.0) to split into two (for nuclear spin=1/2) or more closely spaced levels. This hyperfine splitting is small but confounds attempts to tune the coupling beam and probe beam to a single energy level.
In the prior art, atoms with closely spaced hyperfine split energy levels have been used in EIT by tuning the coupling and probe beams to discrete transitions between the hyperfine levels. However, this approach requires the use of low opacity (and hence low density) samples. This is unfortunate because, for many applications such as nonlinear frequency generation, it is preferable to have high opacity, high density samples. This is because high opacity and high density samples provide higher power capability, and higher frequency conversion efficiencies.
Current techniques for demonstrating EIT in atoms with hyperine structure cannot be extended to high opacities.
It would be an advance in the art of EIT, and particularly in the art of nonlinear frequency generation (a particularly useful application of EIT) to be able to perform EIT with atoms that have hyperfine split energy levels. The ability to perform EIT with materials that have hyperfine split energy levels would greatly increase the number of atomic species that can be used with EIT.
It would be a further advance in the art of EIT to be able to perform EIT with isotopically mixed materials. The ability to perform EIT with isotopically mixed materials would reduce the cost of devices which exploit the phenomenon of EIT.
Further, it would be an advance in the art to be able to perform EIT with high opacity and high density samples that have hyperfine split energy levels.